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Function — Damped Oscillation with its Envelope

A decaying sinusoid drawn against its own envelope, sampled adaptively so the peaks are real peaks rather than whatever a uniform grid happened to land on. The clearest demonstration of why the sampler bisects where the curve bends: at a fixed 100 points this figure shows a different frequency from the one in the formula.

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Damped oscillation3 series (function). x from 0 to 20 — Time. y from -1 to 1 — Displacement. Series: Displacement; Envelope; −Envelope.Damped oscillationy = e^(−t/8) · sin(2πt), with its envelope · 3 series · 807 pointsDisplacementEnvelope−Envelope05101520Time (s)-1-0.500.51Displacement (mm)DisplacementEnvelope−EnvelopeThe curve is sampled where it bends rather than on a uniform grid. A uniform grid at this frequency draws a wave that is not this function and gives no sign that it hasdone so.

Make it your own.

title: Damped oscillation
subtitle: y = e^(−t/8) · sin(2πt), with its envelope
x: Time (s)
y: Displacement (mm)
grid: both
legend: right

plot "Displacement" y = exp(-x/8) * sin(2pi*x) for x in [0, 20]
plot "Envelope" y = exp(-x/8) for x in [0, 20] dashed: yes
plot "−Envelope" y = -exp(-x/8) for x in [0, 20] dashed: yes

note: The curve is sampled where it bends rather than on a uniform grid. A uniform grid at this frequency draws a wave that is not this function and gives no sign that it has done so.